Although few attempts [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]} have been made
to explore the existence of mobility edges in some one- and two-dimensional
(2D) systems, a detailed analysis of it is still missing which essentially
motivates us to investigate this phenomenon with a renewed interest. In this
work we investigate localization properties of a tight-binding ladder
network, constructed by coupling two superlattice chains laterally
(see Fig.1), in presence of an external electric field. Incidentally, many
interesting and novel features of electronic properties have already been
examined in different types of 1D superlattice
chains [8]}, [9]}, [10]}, [11]}, [12]}, which are considered as the
equivalent representation of periodic structures of different metallic
layers [13]}, [14]}, [15]}. The motivation of the present study is
two-fold. Firstly, we intend to reveal the interplay of the superlattice
configuration in the ladder network and the external electric field on
electronic conductance. If the mobility edge phenomenon in such a system
still persists at multiple electron energies like a 1D superlattice chain
in presence of external electric field, then a ladder network of this
particular type, can be used in electronic circuits as a switching device
which might throw new light in the present era of nanotechnology. Secondly,
the ladder networks are extremely suitable for explaining charge transport
through double stranded DNA [16]}, [17]}, [18]}. A clear understanding
of it is highly important due to its potential application in
nano-electronics, especially, to design DNA-based computers. Not only that,
it has also broad applications in biology since it is directly related to
cell division, protein binding processes, etc. Experimental results suggest
that DNA can have all possible conducting properties like,
metallic [19]}, semiconducting [20]}, [21]} or even
insulating [22]}, [23]}. In spite of the numerous experimental and
theoretical [24]}, [25]}, [26]} progress of charge transport through double
helix DNA structures, the conducting nature of DNA molecules are not yet
well explained and a deeper analysis is still needed, in the context of
fundamental physics and technological interest. Nowadays scientists are
trying to develop artificial DNA molecules [27]}, based on DNA
synthesis equipment, those are highly stable and analogous to naturally
occurred DNA molecules. Therefore, the study of electronic transport in a
ladder network comprising of superlattices can give rise significant new
results.
